The Law of Large Numbers (Jump to: Lecture | Video )

The Law of Large Numbers

According to the law of large numbers, as a probability experiment is performed many times, the observed value (usually a mean) will arrive at the expected value.

Imagine a probability experiment where a coin is flipped, and the number of heads is measured:

Figure 1.

As more probability experiments are performed, the actual value will approach the expected value of 0.50. Below are 10 simulated coin flips. As you can see from the line graph on the right, the actual value is approaching the expected value.

Figure 2.

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